%\newcommand\acq		{\mathsf{P}}
%\newcommand\comp	{\mathfrak{c}}
%\newcommand\cycles[1]	{\mathsf{Cycles}{(#1)}}
%\newcommand\eager[1]	{\mathsf{Eager}{(#1)}}
%\newcommand\eenr	{\mathcal{E}}
%\newcommand\enr[1]	{\mathcal{E}_{#1}}
%\newcommand\extens[1]	{\mathsf{Extensions }(#1)}
%\newcommand\extn	{\mathcal{X}}
%\newcommand\lazy[1]	{\mathsf{Lazy}{(#1)}}
%\newcommand\lchist[2]	{{ {#1}\langle#2\rangle }}
%\newcommand\lonepref	{\ppref^1_{N}}
%\newcommand\lpg		{\leadsto_\config}
%\newcommand\lstruc	{\mathcal{L}}
%\newcommand\ltwopref	{\ppref^2_{N}}
%\newcommand\maxspoilers[1]{t^{\spoils}_{#1}}
%\newcommand\move[1]	{\stackrel{#1}{\longrightarrow }}
%\newcommand\myleq	\le
%\newcommand\nat		{\mathrm{I\!N}}
%\newcommand\node[1]	{\mathit{#1}}
%\newcommand\pac		{\mathrel{\nearrow\!\!\!\!\!\nearrow}}
%\newcommand\rd		\propto
%\newcommand\spoils	{\dagger}

% relations
\newcommand\reveals	{\mathrel{\triangleright}}
\newcommand\ac		{\mathrel{\nearrow}}
\newcommand\aco		{\mathrel{/\!/}}
\newcommand\cfl		{\mathrel{\#}}
\newcommand\co		{\mathrel{\parallel}}
\newcommand\eqdef	{\mathrel{:=}}
\newcommand\evolves	{\mathrel{\sqsubseteq}}
\newcommand\evstrict	{\mathrel{\sqsubset}}
\newcommand\ispref	{\mathrel{\preceq}}
\newcommand\icause	{\mathrel{<_i}}
\newcommand\ifft	{\mathrel{\text{ iff }}}
\newcommand\nco		{\mathrel{\not\!\!\;\,\co}}

\newcommand\extreveals	{\mathbin{-\hspace{-2.5mm}-\hspace{-2.0mm}\reveals}}

% operators
\newcommand\merge[1]	{\mathop{\mathfrak{Merge}} (#1)}
\newcommand\od[1]	{\mathop{\mathrm{od}} (#1)}
\newcommand\amo[1]	{\mathop{\text{AMO}} (#1)}
\newcommand\bigo[1]	{\mathop{\mathcal{O}} (#1)}
\newcommand\progloop[1]	{\mathop{\mathit{ploop}} (#1)}
\newcommand\allhist[1]	{\mathop{\mathit{Hist}} (#1)}
\newcommand\compt[1]	{\mathop{\mathit{compat}} (#1)}
\newcommand\conc[1]	{\mathop{\mathit{conc}} (#1)}
\newcommand\conf[1]	{\mathop{\mathit{conf}} (#1)}
\newcommand\cut[1]	{\mathop{\mathit{cut}} (#1)}
\newcommand\explain[1]	{\mathop{\mathit{expl}} (#1)}
\newcommand\lpo[1]	{\mathop{\mathit{lpo}} (#1)}
\newcommand\marking[1]	{\mathop{\mathit{mark}} (#1)}
\newcommand\obser[1]	{\mathop{\mathit{obs}} (#1)}
\newcommand\peel[2]	{\mathop{\mathit{peel}}_{#2} (#1)}
\newcommand\peelast[1]	{\mathop{\mathit{peel}}^* (#1)}
\newcommand\reach[1]	{\mathop{\mathit{reach}} (#1)}
\newcommand\runs[1]	{\mathop{\mathit{runs}} (#1)}
\newcommand\sfp[1]	{\mathop{\mathit{pred}} (#1)}
\newcommand\spoilers[1]	{\mathop{\mathit{spoilers}} (#1)}
\newcommand\state[1]	{\mathop{\mathit{state}} (#1)}
\newcommand\succexpl[1]	{\mathop{\mathit{succexpl}} (#1)}
\newcommand\trim[2]	{\mathop{\mathit{trim}_{#2}} (#1)}
\newcommand\trimast[1]	{\mathop{\mathit{trim}}^* (#1)}
\newcommand\depth[1]	{\mathop{\mathit{depth}} (#1)}

\newcommand\sem[1]	{\mathrm{[\![{#1}]\!]}}
\newcommand\hist[2]	{{ {#1}[\![#2]\!] }}
\newcommand\cont[1]	{\underline{#1}}
\newcommand\post[1]	{#1^\bullet}
\newcommand\pre[1]	{{}^\bullet#1}
\newcommand\support[1]	{\bar{#1}}

\newcommand\FIXME[1]	{\texttt{FIXME: #1}}
\newcommand\anc[1]	{{#1}^\uparrow}
\newcommand\unf[1]	{\mathcal{U}_{#1}}
\newcommand\unr[1]	{\mathcal{M}_{#1}}
\newcommand\var[1]	{\mathsf{#1}}
\newcommand\mer[1]	{\mathcal{Q}_{#1}}
\newcommand\hst[1]	{\mathcal{H}_{#1}}
\newcommand\trunc[1]	{\mathcal{T}_{#1}}
\newcommand\htrunc[1]	{\widehat{\mathcal{T}}_{#1}}
\newcommand\pref[1]	{\mathcal{P}_{#1}}

% abbreviations
\newcommand\precutoff	{\text{$\prec$-cutoff}}
\newcommand\phiasym	{\phi_{\ppref}^\text{asym}}
\newcommand\phicausal	{\phi_{\ppref}^\text{causal}}
\newcommand\phidead	{\phi_{\ppref}^\text{dead}}
\newcommand\phidis	{\phi_{\ppref}^\text{dis}}
\newcommand\phimark	{\phi_{\ppref}^\text{mark}}
\newcommand\phip	{\phi_{\ppref}}
\newcommand\phisym	{\phi_{\ppref}^\text{sym}}
\newcommand\mcitomp	{\textsc{Mci2mp}\@\xspace}
\newcommand\minisat	{\textsc{MiniSat}\@\xspace}
\newcommand\mole	{\textsc{Mole}\@\xspace}
\newcommand\prcompress	{\textsc{PRCompress}\@\xspace}
\newcommand\clp		{\textsc{Clp}\@\xspace}
\newcommand\cmerge	{\textsc{Cmerge}\@\xspace}
\newcommand\cunf	{\textsc{Cunf}\@\xspace}
\newcommand\cosyverif	{\textsc{Cosyverif}\@\xspace}
\newcommand\coloane	{\textsc{Coloane}\@\xspace}
\newcommand\tapaal	{\textsc{Tapaal}\@\xspace}
\newcommand\cunft	{Cunf~Tool}
\newcommand\cna		{\textsc{Cna}\@\xspace}
\newcommand\punf	{\textsc{Punf}\@\xspace}
\newcommand\salpha	{\ppref_\alpha}
\newcommand\spcutoff	{\text{sp-cutoff}}
\newcommand\id		{\textit{id}}
\newcommand\cep		{EP}

\newcommand\ppref	{\mathcal{P}}
\newcommand\qpref	{\mathcal{Q}}
\newcommand\con		{\mathcal{C}}
\newcommand\N		{\mathbb{N}}
\newcommand\Q		{\mathbb{Q}}
\newcommand\R		{\mathbb{R}}
\newcommand\obs		{\mathbb{O}}
\newcommand\hhat	{\widehat h}
\newcommand\ehat	{\widehat e}
\newcommand\chat	{\widehat c}
\newcommand\Cohat	{\widehat \con}
\newcommand\Hihat	{\widehat H}

\newcommand\pp		{pp.\@\xspace}
\newcommand\viz		{viz.\@\xspace}
\newcommand\vs		{vs.\@\xspace}
\newcommand\wlogg	{w.l.o.g.,\xspace}
\newcommand\aka		{a.k.a.\xspace}
\newcommand\wrt		{w.r.t.\@\xspace}
\newcommand\cf		{cf.\@\xspace}
\newcommand\Wlog	{W.l.o.g.,\xspace}
\newcommand\al		{al.\@\xspace}
\newcommand\eg		{e.g.\@\xspace}
\newcommand\etc		{etc.\@\xspace}
\newcommand\ie		{i.e.\@\xspace}
\newcommand\naive	{na{\"\i}ve\xspace}

% miscellaneous
\newcommand\cod[1]	{\texttt{#1}}
\newcommand\tup[1]	{\langle#1\rangle}
\newcommand\set[1]	{{\{ \, #1 \, \mathclose \}}}
\newcommand\eqtag[1]	{\hfill{} \refstepcounter{equation} \label{#1} (\arabic{equation})}

\newtheorem{cor}	{Corollary}
\newtheorem{defn}	{Definition}
\newtheorem{lemma}	{Lemma}
\newtheorem{prop}	{Proposition}
\newtheorem{remark}	{Remark}
\newtheorem{theorem}	{Theorem}

% a  appendix
% c  chapter
% o  corollary
% d  def
% e  equation
% f  figure
% l  lemma
% p  proposition
% r  remark
% s  section
% t  table
% h  theorem

